Find the principal value of each of the following :

Question:

Find the principal value of each of the following :

$\cot ^{1}(-1)$

 

Solution:

$\cot ^{-1}(-1)=\pi-\cot ^{-1}(1)\left[\right.$ Formula: $\left.\cot ^{-1}(-x)=\pi-\cot ^{-1}(x)\right]$

$=\pi-\frac{\pi}{4}$

$=\frac{3 \pi}{4}$

 

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